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Defeat to Portsmouth last weekend heightened frustration among City supporters as Norwich suffered a fifth successive Championship loss, leaving them one point and one place above the relegation zone.
Martin, who came through City's academy before making more than 100 appearances for his boyhood club, believes Clement retains credit after demonstrating his ability to string results together last season.
Despite acknowledging that patience will not last indefinitely, Martin would stick with the City boss .
"There is an expectation there with Norwich's recent history in terms of promotions, the fans will probably have that as a target," Martin said.
"I think Philippe Clement has got some credit in the bank after last season and the runs that they put together. But how long that lasts is another thing. You might only get three or four more games.
"They've lost six in a row. It doesn't look great for anybody, does it? Even if you've done very well last season and shown that you understand the league and can put a team together that's able to be consistent and win games.
"So I would stick by him, but again, the million-dollar question is for how long? How many more games do you give him? If they don't get a couple of wins out of the next three or four games, then I'm sure questions will start to be asked more and more."
Martin admits City's struggles have confounded his pre-season expectations, having anticipated Clement's side would build on last year's progress and challenge towards the top end of the Championship.
"Do you know what? It's a real surprise for me, actually, after seeing Norwich last season. I did cover one of their games against Stoke and they were a bit toothless, to be honest. They didn't really look like they had much going forward.
"So it's actually really surprising to me. I thought Norwich would be up and challenging around the play-offs early on this season, but it'll be interesting to see how the season develops," Martin told the Pink Un via Lyllo Casino.
Chris Martin has been surprised by Norwich City's slow start to the season. (Image: Alex Broadway/Focus Images Ltd)
"I do think that they've got a good squad and a good manager, and they showed last year that they're able to put results together. But obviously, it's tough. The Championship is always a really tough division.
"Momentum, both good and bad, can be a big thing. You see teams that are fancied to have a good season and they just cannot get out of that rut of losing games. So you want to arrest that slide pretty quickly, I would say.
"Have they scored enough goals? Probably not. I think defensively as well, from when I've seen them, they're a little bit too easy to score against. I think that'll be frustrating for the manager and something for them to look at. They need to be a bit tougher to score against."